On the Diffraction by Biperiodic Anisotropic Structures

Author: Schmidt G.

Source: Applicable Analysis, Volume 82, Number 1, January 2003 , pp. 75-92(18)

Publisher: Taylor and Francis Ltd

Abstract:

This article studies the scattering of electromagnetic waves by a nonmagnetic biperiodic structure. The structure consists of anisotropic optical materials and separates two regions with constant dielectric coefficients. The time harmonic Maxwell equations are transformed to an equivalent strongly elliptic variational problem for the magnetic field in a bounded biperiodic cell with nonlocal boundary conditions. This guarantees the existence of quasiperiodic magnetic fields in H¹ and electric fields in H(curl) solving Maxwell's equations. The uniqueness is proved for all frequencies excluding possibly a discrete set. The analytic dependence of these solutions on frequency and incident angles is studied.

Keywords: Maxwell equations; Diffraction; Strongly elliptic variational formulation; Existence and uniqueness of solutions

Document Type: Research article

DOI: http://dx.doi.org/10.1080/000368103762985796

Affiliations: 1: Weierstrass Institute of Applied Analysis and Stochastics D-10117 Berlin, Mohrenstr. 39, Germany

Publication date: 2003-01-01

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